Potential Energy
Height Work is a process. When a box is lifted, work is done on the box. At the end, the box is resting – no kinetic energy. Where did the work go? y1y1 F = mg h y2y2
Energy Change The state of the object changes The box is higher after the work was doneThe box is higher after the work was done Work can be stored in a new positionWork can be stored in a new position y1y1 h y2y2
Work from Height The box can move down from its height and do work. The work done by gravity is converted to kinetic energyThe work done by gravity is converted to kinetic energy The work done by gravity is opposed by some other force, and less work is doneThe work done by gravity is opposed by some other force, and less work is done y1y1 F = mg h y2y2
Elastic Energy As a spring compresses work is done. Work done by gravity on the ball, W = mghWork done by gravity on the ball, W = mgh Work done by the spring on the ball, W = (1/2)kx 2Work done by the spring on the ball, W = (1/2)kx 2 Work done by the spring to return the ball, W = (1/2)kx 2Work done by the spring to return the ball, W = (1/2)kx 2 There is an elastic energy. -y F g = mg F s = k( y)
Potentials Energy due to position is called potential energy (U). An object has the potential to do workAn object has the potential to do work Since the work isn’t done yet, U = W int. W int is the force acting internally to the objectW int is the force acting internally to the object The potential energy of gravity: U = mgy The potential energy of a spring: U = (1/2)kx 2
No Absolute The work done on an object from a force only reflects a change in the state of the object. Work is a processWork is a process Energy is a stateEnergy is a state Potential energy reflects the work that may be done. The point U = 0 is arbitraryThe point U = 0 is arbitrary For instance, experiment at the top of a building of height h, U = mg(y+h) = mgy + mgh = mgy + CFor instance, experiment at the top of a building of height h, U = mg(y+h) = mgy + mgh = mgy + C next